Numerical solution of the direct and inverse problem of electrical exploration using the finite element method

Abstract

This article discusses the results of solving the problem of electrical exploration using direct current. The developed methods and algorithms for solving the direct and inverse exploration tasks are tested on several inhomogeneous models of the environment. The task is considered in three-dimensional approximation. To solve using the finite element method. Based on direct problem algorithm, a method for solving the inverse problem was implemented, which consists in finding the minimum of the deviation functional, which in turn leads to the multiple solution of the direct problem. The results were analyzed in order to identify disadvantages and advantages. An analysis was also made of the search time for optimal solutions, and the dependence of the accuracy of the solution on the thickening of the mesh when solving the problem by the finite element method was discussed.